Abstract
In the present paper, we apply the method of invariant sets of descending flow to establish a series of criteria to ensure that a second-order nonlinear functional difference equation with periodic boundary conditions possesses at least one trivial solution and three nontrivial solutions. These nontrivial solutions consist of sign-changing solutions, positive solutions and negative solutions. Moreover, as an application of our theoretical results, an example is elaborated. Our results generalize and improve some existing ones.
2000 Mathematics Subject Classifications:
Acknowledgements
The author gratefully acknowledges the two anonymous reviewers for their careful reading and valuable comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the author.